These arent that powerful, but they are the best, for muk, as his sp. attack is low.

Or You Could do this strategy: First, Use Toxic(The Damaging Move Of This Set), Minimize(So Muk Cant Be Hit, Use Multiple Times), Screech(Sets Up Swagger, Which Does More Damage To Themselves, if they have low defense), And Then Swagger(After Screech, If They Hurt Themselves, They Will Lose Half Their Health. Plus, They Still Cant Hit Muk Because of Minimize, so even if they don't hurt themselves in confusion, they still don't kill muk.).

Gunk Shot is high powered STAB. You'll want it over Poison Jab because you won't be able to much count on a Super-effective hit, meaning you'll need high base power. Shadow Sneak provides priority. Brick Break provides type coverage. Curse can make Muk a nice physical tank. It isn't like you'll be needing Speed. Black Sludge provides you with healing. Since it will actually harm most foes to be holding this, you don't need Sticky Hold, and Stench is just bad, so Poison Touch is the ability. EVs give you nice defenses, and allow you to do good damage.

This guy is one of my favourite OG Pokemon, he is a pile of purple gelatinous substance, how awesome is that?
Anyway, Muk has decent defenses, high HP, and pretty good Attack, I think he does best with high powered moves to accentuate that attack. First, we have Poison Jab or Gunk Shot for STAB, the typical "power vs accuracy" debate, I prefer accuracy, so I go with Poison Jab. Focus Punch makes the set, it has 150 Power is isn't hindered by Muk's poor speed stat. Shadow Sneak has priority, is physical, and provides full neutral coverage with Focus Punch, it also hits Psychic types pretty hard; Payback is also viable, as Muk is slow, and it has almost as good a coverage, with a little more power. Substitute makes the set work as it protects Muk from flinching on Focus Punch, Muk can put up huge 101 Subs that can't be broken by simply Seismic tossing them.
EVs give it 404 HP (101 Sub), max attack, and a heightened SpDef for taking blows. Black Sludge is like Leftovers for poison types, I often use it to avoid Item Clauses, leftovers is also pretty much the same. Sticky Hold is the only worthwhile ability on this set as Stench is useless and Poison Touch doesn't work with two of the attacks...

Poison Jab - If you use sludge bomb instead-You're a little STUPID!
Brick Break - Coverage is the word.
Toxic - To kill your enemys with pollution.
Acid Armor - Your very hard to kill after using this attack several times.

The Muk can hold an Life Orb, Leftovers or an Quick Claw. It's your opinion!

Muk, by my point of view, is a good tank. 105 base HP and Attack, 100 base SpD, and 50 base Speed

Ability: Sticky Hold- prevents Trick sets and it is the only good ability available unless they come out with Poison Touch Grimer

Item: Leftovers/Sitrus Berry/Black Sludge/Life Orb- heal the tank after taking damage or power up Muk even more, ur choice

Poison Jab- reliable STAB move with a good chance to poison

Ice Punch- cover weakness to ground types and take out dragon's, flying types, and grass types

Curse- Muk is already slow and this move will up ur already great attack and decent defense stats

Payback/Shadow Sneak/Shadow Punch- with the boosted attack and lowered speed from curse, payback will double in power and receive the boost from curse, shadow sneak receives the boost from curse and gives you priority, and shadow punch is more powerful than shadow sneak, receives boost from curse, and never misses (all moves defeat psychics, its really ur choice)

Poison Jab: It has 30% to poison oppenent and it is good for physical poison type Pokemon like Toxicroak.
Ice Punch: Cover Muk's weakness.
Shadow Punch: Cover Muk's another weakness and never miss.
Brick Break/Facade: Brick Break is for Steel Type Pokemon, Facade is for combo with Poison Jab's poison.

A special tank that can freely set up on many threats if needed, 1 acid armor puts muks defenses higher than its special. This makes it much harder for muk to be countered. Poison jab is the primary move on the set, but PUP makes muk a big sweep threat and allows him to get past some fragile steel types with relative ease. And hit hard with poison jab or shadow sneak on the next Pokemon.

It isnt Op by any means but it does work well and can function as a special wall without any time invested in its set up moves.

I switched in muk on a galvantula, acid armor on the switch PuP was a 2hko on the in coming ambipom. Taking 30%(if that) from doubleHit(first turn he used taunt) after black sludge. He then took on a mega blazekien and lived the flare blitz to ohko with poison jab.
That is testament to the bulk of muk.

Stockpile if you want both defenses raised, curse if you want the attack raise.
Poison Jab is STAB, Toxic for stalling or Haze to prevent Pokemon from setting up on you. Fire punch is to hit steel types.

Once you have a Trick Room set up, simply switch this guy in and wreak havoc. With such low speed halved by the Iron Ball this Muk will definitely move first. His main STAB move can be either Poison Jab or Gunk Shot, depending upon whether you prefer power or accuracy. Ice Punch covers your Ground weakness, and Flinging an Iron Ball has 130 base power while covering your Psychic weakness. Finally, the good bulk of this set should allow you to survive long enough to Disable any moves you can't take many of or wait till the last second to Explode all over your adversaries. This set works well in Doubles, too since Gunk Shot hits both opponents at once.

Payback-(because muk is so slow. And muks attack is pretty decent)
Toxic
Acid armour (setting up the defensive wall)
Minimize (makes him almost untouchable)

I always switch in with muk when the opposing Pokemon is for sure a special attacker. Then I set up with minimize and acid armour, so that he will rarely ever get hit and when it does it doesn't do much. Plus he is holding black sludge so he regenerates health. The sticky hold ability ensures that he will not loose his item because he really relies on it. Then use toxic and wait out the slow fainting of the opponent. But for those pesky steel types, I use payback because dark type moves now have normal damage on them. I 2 hit koed a metagross so I am pretty pleased with this strategy. It has gotten my out of pleanty of tough battles.
The only thing I have trouble with is when he gets burned, but with the black sludge it takes the burn a lot longer to ko him. Hope you like my Muk!